You love someone, you open yourself up to suffering, that's the sad truth.
Maybe they'll break your heart, maybe you'll break their heart and never be able to look at yourself in the same way. Those are the risks. That's the burden.
You see two people and you think, they belong together, but nothing happens. The thought of loosing so much control over personal happiness is unbearable.
That's the burden. Like wings, they have weight, we feel that weight on our backs, but they are a burden that lifts us. Burdens that allow us to fly.